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In [[mathematics]], '''Poinsot's spirals''' are two [[spiral]]s represented by the [[polar equation]]s
 
:<math> r = a\ \operatorname{csch} (n\theta) </math>
:<math> r = a\ \operatorname{sech} (n\theta) </math>
where csch is the [[hyperbolic cosecant]], and sech is the [[hyperbolic secant]].<ref name=Lawrence1972>{{cite book|last=Lawrence|first=J. Dennis|title=A Catalog of Special Plane Curves|year=1972|publisher=Dover|location=New York|pages=192–194|isbn=0486602885}}</ref> They are named after the French mathematician [[Louis Poinsot]].
 
{{multiple image
|align= center
|footer = Examples of the two types of Poinsot's spirals.
|image1 = Poinsot2.svg
|width1 = 300
|alt1 = The Poinsot spiral r=csch(θ/3).
|caption1 = The Poinsot spiral r=csch(θ/3).
|image2 = Poinsot1.svg
|width2 = 285
|alt2 = The Poinsot spiral r=sech(θ/3).
|caption2 = The Poinsot spiral r=sech(θ/3).
}}
 
==See also==
[[Cotes' spiral]]
==References==
{{reflist}}
 
{{geometry-stub}}
[[Category:Spirals]]

Revision as of 23:38, 21 January 2014

In mathematics, Poinsot's spirals are two spirals represented by the polar equations

r=acsch(nθ)
r=asech(nθ)

where csch is the hyperbolic cosecant, and sech is the hyperbolic secant.[1] They are named after the French mathematician Louis Poinsot.

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See also

Cotes' spiral

References

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